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Old English wyrgan "to strangle," from West Germanic *wurgijanan (cf. Middle Dutch worghen, Dutch worgen, Old High German wurgen, German würgen "to strangle," Old Norse virgill "rope"), from PIE *wergh- "to turn" (see wring). Related: Worrisome; worrying.
The oldest sense was obsolete in English after c.1600; meaning "annoy, bother, vex," first recorded 1670s, developed from that of "harass by rough or severe treatment" (1550s), as of dogs or wolves attacking sheep. Meaning "to cause mental distress or trouble" is attested from 1822; intransitive sense of "to feel anxiety or mental trouble" is first recorded 1860.
1804, from worry (v.).
To evade or avoid an unpleasant situation, esp by ignominious means: This time we have him dead to rights, and he won't worm out of it (1893+)